__ B -_

ELSEVIER Nuclear Instruments and Methods in Physics Research A 403 (1998) 98-l 14

NUCLEAR INSTRUMENTS

8 METHODS IN PHYSICS RESEARCH

SectIon A

Evaluation of Fermi read-out of the Atlas Tilecal prototype

Z. Ajaltouni”, F. Albiolb, A. Alifanov”, P. Amarald’qd2, D. Amelin’, A. Amorimd’.d2, K. Andersonf, C. Angelinig, S. Agnvallh, A. Antola’, F. Astesanj, A. Astvatsaturovk,

D. Autierog, F. Badaud”, G. Barreirad’, R. Benetta’, S. Berglundh, G. Blanchot”, E. Blucherf, C. Blajn, P. Bode”, A. Bogush’, C. Bohmh, V. Boldea”, 0. Borisovk,

M. Bosmanm, N. Bouhemaid”, P. Brettea, L. Breveglieri’, C. Brombergp, M. Brossarda, J. Budagovk, L. Calobaq, J. Carvalhod3, P. Casado”, A. Castera’, P.W. Cattaneo”“,

M. Cavalli-Sforza”, V. Cavasinnig, R. Chadelas”, J.-C. Chevaleyre”, I. Chirikov-Zorink, G. Chlachidzek, M. Cobal’, F. Cogswell”, F. Colacod4, S. Constantinescuk, D. Costanzog, M. Crouau”, L. Dadda’, F. Daudona, J. David’, M. Davidd1Td2, T. Davidek’, J. Dawson’, K. De”, T. Del Preteg, A. De Santog, B. Di Girolamog, S. Dita”, J. Dolejsi’, Z. Dolezal’, R. Downings, J.-J. Dugne”, I. Efthymiopoulos”, M. Engstriimh, D. ErredeS, S. Errede”, H. Evansf, A. Fenyuk”, A. Ferrerb, A. Fristedth, V. Flaminiog, E. Gallas’, M. Gasparq, 0. Gildemeister’, M. Givoletto”, V. Glagolevk, V.G. Goggi’, A. Gomesd1.d2, S. Gong”,

Y. Gauze, V. Grabsky”, M. Grieco”, H. Hakopian”, M. Haney”, M. Hansen’, S. Hellmanh,

A. Henriques d1 H Hentzell”, T. HolmbergY, S. Holmgrenh, P.F. Honoreb, J. Huston”, , .

Yu. Ivanyushenkov”, K. Jon-Andh, A. Justem, S. Kakurink, G. Karapetian’, A. Karyukhin’, . Kerek”, Yu. Khokhlov”, S. Kopikov’, M. Kostrikov’, V. Kostyukhin’, V. Kukhtink,

Y. Kulchitsky”, W. Kurzbauer’, S. Lamig, C. Landi”, V. Lapin”, C. Lazzeronig, A. Lebedevk, R. Leitner’, J. Li”, M. Lippi”, 0. Ledortzj, B. Lofstedt’, Yu. Lomakink, 0. Lomakinak,

M. Lokajicek”,“, B. Lund-Jensen”, A. Maiodl.d’, S. Malyukovk, R. Marianibb, F. Marroquin q, J.P. Martinsd1*d2, E. Mazzonig, F. Merrittf, B. Michel”, R. MillerP,

I. Minashvilik, Ll. Miralles”, E. Mnatsakanian”, G. Montarou”, S. Mottobb, G.S. Muanzaa, S. Nemecekaa, M. Nessi’, A. odmarky, A. 0nofred3.d4, S. Orteu”, C. Padilla”, D. Pallin”, D. Panteak.“, J. Patriarcadl, A. Pereiraq, J.A. Perlasm, S. T. Persson“, P. Petit”, J. Pilcher’, J. Pinhaod3, L. Poggioli’, S. Poirota, G. Polesello’, L. PriceU, J. Proudfoot”, 0. Pukhovk,

G. Reinmutha, G. Renzonig, R. Richard+‘, I. Riu”, V. Romanovk, B. Ronceuxm, V. Rumyantsev’, N. Russakovichk, M. Sami’, H. Sandersf, J. Santosd’, A. Savoy-Navarroj,

L. Sawyer”, L.-P. Says”, Ph. Schwemlingj, J.M. Seixasq, B. Selldenh, A. Semenovk, A. Shchelchkovk, M. Shochetf, V. Simaitis”, A. Sissakiank, A. Solodkov’, 0. Solovianov’,

*Corresponding author. Tel.: + 39 382 50 75 78; fax: + 39 382 42 32 41; e-mail: cattaneo@pv.infn.it

016%9002/98/$19.00 ((31 l9Y8 Elsevier Science B.V. All rights reserved

PI1 SOl68-9002(97)01086-3

Z. Ajaltouni et al.lNucl. Instr. and Meth. in Phys. Res. A 403 (1998) 98-114 99

P. Sonderegger’, K. Soustruznik’, R. Stanek”, E. Starchenkoe, R. Stefanelli’, R. Stephens”, M. Suk’, R. SundbladY, C. Svenssoncc, F. Tang’, S. Tardellh, P. Tas’, F. Teubert”, J. Thaler”, S. Tokardd, N. Topilink, Z. Trka’, A. Turcotf, M. Turcotte”, S. Valkar’, M.J. Varandasd’.d2, A. Vartapetiar?, F. Vazeille”, V. Vinogradovk, F. Vivaldibb, S. Vorozhtsovk, D. Wagner’, A. White’, H. Woltersd4, N. Yamdagnih, G. Yarygink, C. YosefP, J. Yuan”, A. Zaitseve,

M. Zdrazil’

a LPC Clermont-Ferrand, Universid Blaise PascallCNRS-INZP3, France b IFIC Valencia, Spain

‘Institute of Physics ASB. Minsk, Belarus “LIP-Lisbon, Portugal

d2 FCUL-Univ. c>f Lisbon. Portugal “LIP and FCTUC-Univ. of Coimbra, Portugal

d4 Univ. Catblica Figueira da Fez. Portugal e Institute for High Energy Physics. Protvino. Russia

’ Universiv q/Chicago. USA g Pisa Universiv and fNFN. Pisa, Ita&

‘Stockholm University. Sweden ’ Politecnico di Milano, and INFN, Pavia. Italy

’ LPNHE Universites Paris VI-VII, Paris. France k JINR Dubna. Russia

’ CERN, Geneva, Switzerland m lnstitut de Fisica d’Altes Energies, Universitat Autdnoma de Barcelona, Spain

n Institute of Atomic Physics, Bucharest, Romania a Industrial Microelectronics Center. University of Linkiiping, Sweden

PMichigan State Universit): USA q COPPE/EEJUFRJ, Rio de Janeiro, Brazil r Pavia Universiv and INFN. Pacia, Itab

’ University of Illinois. USA t Charles Universip. Prague, Czech Republic

u Argonne National Laboratory, USA ’ Universi@ of Texas a! Arlington, USA

w C.A.E.N. S.p.A.. Viareggio, Itab ’ Yerevan Physics Institute. Armenia

y SiCon AB. Linkiiping. Sweden ‘Royal Institute of Technology. Stockholm, Sweden

aa Academy of Science. Prague. C:ech Republic bb C.A.E.N. Microelectronics. Pisa. Ita&

CC University of Linkcping. Sweden dd Comenius Unir. Bratislaca. Slovakia

Received 4 July 1997

Abstract

Prototypes of the FERMI system have been used to read out a prototype of the ATLAS hadron calorimeter in a beam test at the CERN SPS. The FERMI read-out system, using a compressor and a sampling ADC, is compared to a standard charge integrating read-out by measuring the energy resolution of the calorimeter separately with the two systems on the same events.

Signal processing techniques have been designed to optimize the treatment of FERMI data. The resulting energy resolution is better than the one obtained with the standard read-out. C: 1998 Elsevier Science B.V. All rights reserved.

Keywords: Calorimetry; Signal processing; Read-out electronics

100 2. Ajaliouni et al./Nucl. Instr. and Meth. itt Phw Res. A 403 (1998) 98-114

1. Introduction 2. The Fermi analog channel

This paper summarizes the evaluation of the FERMI system prototypes used to read out a prototype of the ATLAS hadronic barrel calori- meter, Tilecal, during the July 1995 beam tests at the CERN SPS.

Tilecal is an iron-scintillator sampling hadron calorimeter with the distinctive feature that the scintillating tiles are oriented parallel to the im- pinging particles.

The major goals of the calorimeter are to identify

jets and to measure their energy and direction, to measure the total missing energy and to enhance the particle identification of the electromagnetic calorimeter by measuring energy leakage and shower isolation. Additionally, the hadronic calori- meter should absorb all particles before they reach the muon chamber system, and provide low pT muon identification.

The FERMI project was started in 1990 with the aim to design a read-out system for calorimetry at high-luminosity hadron machines, based on the concept of fast digitization of the analog signal followed by digital signal processing. For applica- tions at the LHC, the basic requirement is to match the dynamic range implied by the physics (15-16 bits) with the ADC range (lo-12 bits) technically feasible at the required digitization rate (40 MHz). This is achieved by a dynamic non-linear compres- sor. The project is described in detail in Refs. [6,7] and references therein. A schematic layout of the system is shown in Fig. 1.

To meet these goals the design aims at a resolu-

tion of SO%/JE@3%, a linearity of l-2% up to a few TeV with a granularity in pseudo-rapidity and azimuthal angle of 8~ x A4 = 0.1 x 0.1.

The need to resolve low-energy muons sets the

lower end of the dynamic range. 15 ADC counts are required for a muon depositing 0.5GeV per read- out cell. From simulations, the maximum expected energy per cell in Tilecal is about 2 TeV, at a rate of a few events per year. This gives a required dynamic

range of approximately 21h. The overall performance of the Tilecal prototype

is reported in Refs. [l-4] and the current status of the project is described in detail in the ATLAS Tile Calorimeter Technical Design Report [IS].

The FERMI prototypes consist of an analog compressor and a 10 bits sampling ADC operating at 40 MHz on a custom VME board.

The shaper takes input from either the photo- multiplier or the charge injection circuitry and de- livers a 200ns wide pulse (FWHM) in the O-2V range on the output. The compressor, schemati- cally shown in Fig. 2, subsequently takes this signal and performs a non-linear transformation, com- pressing the signal according to an approximately piecewise linear transfer function. producing on the output a signal in the O-2 V range.

The compressed signal is sampled at 40 MHz frequency by a custom-designed 10 bit sampling ADC [S], which feeds a 256 sample FIFO register. A trigger starts the digitization at the next ADC clock cycle. The timing of the trigger is such that approximately 20 samples are taken before the peak. In total, 60 consecutive ADC samples are taken to contain the pulse. The FIFO is then read out by the standard DAQ and data are stored

on tape. In Fig. 3 four single charge injection events of

different amplitudes are shown. The regions of different gain are clearly shown on the two

largest pulses, while the smallest is uncompressed,

r charge injection

I I r 1

photo-multiplier shaper compressor ADC pipeline

Fig. 1. Block scheme of the read-out system. The digital pipeline has not been part of these tests.

1800

1600

1400

1200

1 cm0

800

600

400

200

0

Input rn”

Fig. 2. Concept of the compressor. This circuitry forms a sum of the outputs from four linear amplifiers with gams approximately 1 X.5.

1.3. 0.14 and 0.09 and upper cutoffs on the input voltage of 60. 470 and 1200mV. respectively. The fourth amplifier spans the full

?OOOmV input range of the compressor. To the right. a typical transfer function as measured in the laboratory.

PPG data for PM85 - single events

400

300

200

100

0 t

Ampl. 9

$ 450 2 P 400

9

x

RSO

< 300

210

200

110

100

50

0 20

S%pling nunil

15

d

Fig. 3. Example of four single charge injection events. Amplitude 3 1s in the first linear region: amplitude h peaks at the fir51 “knee”. Y at

the second and 15 in the third region. Note the different scales.

102 2. Ajaltouni et al. jNuc1. Instr. atrd Meth. in Phw Res. A 403 (199X) 9X-I 14

being totally within the first linear region of the compressor.

The compressed signals have to be relinearized before reconstruction of the calorimeter showers. This is conveniently done by mean of a lookup table for each channel. One of the main goals of this study is to devise and evaluate algorithms for the construction of these lookup tables from charge injection data. The design of the FERMI system foresees implementation of the lookup tables in

hardware, thus allowing an online linearization and correction of the data.

3. Testing Fermi in a particle beam with Tilecal

A small number of prototypes of the FERMI analog channels were tested in 1994 in 300 GeV beams with both hadronic and electromagnetic barrel calorimeter prototypes [9-l 11. In July 1995 a stack of five prototype modules of the ATLAS Tilecal Calorimeter was tested in beam at the

CERN SPS.

3.1. Description of the one meter Tilecal prototype

Each prototype module (see Fig. 4) corresponds to a 2rc/64 slice in azimuth (4), with a front face of f 50cm in z (horizontal direction, perpendicular

to the beam) and + 1Ocm in the 4 direction. In the radial direction (along the beam) the modules measure 180 cm, corresponding to nine nuclear in-

teraction lengths, 2. The five modules were stacked, covering together a @angle of approx. 26’. Each module has four radial (depth) segmentations cor- responding to 1.5, 2.0. 2.5 and 3.0 1, (30, 40, 50 and 60cm). In the z-direction each sampling is divided into five cells. Towers are defined as cells with the same z and 4. Fig. 4 is a sketch of the cell layout for one module.

Each cell is read out independently from both sides, giving a total of 40 read-out channels per module. The central module in the stack was equip- ped with active splitters and double sets of read-out electronics, one based on standard integrating 12- bit ADCs, and one based on the FERMI concept. The numbers in Fig. 4 correspond to channel num- bers in the central module. Four channels (117-l 20)

row I-S

Fig. 4. Cell layout and dm~ensions of a I m Tilecal prototype

module. Numbers refer to the PMT (channel) numbers of the

central module.

were not equipped with FERMI, furthermore nine channels (82, 83,90-92, 109-l 12) were faulty or not well calibrated, leaving 27 FERMI channels for this analysis.

3.2. Beam line

Measurements were performed in the H8 beam line of the SPS at CERN. The stack of five proto- type modules was mounted on a scanning table which allowed precise movements in 0,4 and z. The beam line (Fig. 5) was instrumented with two beam chambers defining the impact point and three scin- tillators for triggering.

The runs considered for the analysis are de- scribed in Table 1 and in Fig. 7.

3.3. Precisiorl pulse genewtor

The Precision Pulse Generator (PPG) used for the 1995 run was designed for the calorimeter of the UA2 experiment [12]. Three eight-channel PPG- modules are fed a 1OOV DC voltage. This voltage can be subdivided in 14 steps, using a resistor ladder, according to a logarithmic scale. The PPG HV feeds a capacitor on each channel which, on

- #iI3 - __~-----_---~- -------- i Mubn wall- 5 Module Detector

BC2

- _- 1 I __-_

s2

_t___

s3

Not to scale

BCl

;!I

beam tin ----_ - - _+_-

Sl

Fig. 5. Test beam layout for the 1995 stand alone test beam

Table I

RUNS and orientations of the calorimeter

RUH No. events Beam typz H (deg) z (cm)

334x4 15205 300 GrV K- + 10 -6

33485 15143 300 GeV x- + 10 -8 334X6 15172 300 GeV r[- + 20 - I8

33487 15150 300GeVrr- +?O -20 334x9 : I5000 300 GeV R- + 30 - 36

a remote command, is shorted by an Hg relay. Each

channel is connected to a PPG box which in turn either connects ten PMTs to their respective ADC- channels or distribute the signal from one PPG channel to ten ADC-inputs (see Fig. 6).

4. Techniques for Fermi calibration

In the 1994 beam tests the number of calorimeter channels equipped with FERMI was not large enough to exploit the energy resolution of the calori- meter as a tool to measure the performance of the FERMI electronics. Therefore. other techniques were developed to infer the behaviour of FERMI. Several of these techniques provide valuable information on the detailed features of single channels and have been refined in the subsequent analysis [13,14].

The standard read-out, using charge Integrating ADCs, provides a single number for the estimation of the energy per read-out channel. To calibrate these electronics it is sufficient to measure for each channel the pedestal and a calibration curve. by

injecting a set of pulses of known charge. The FERMI read-out is different in two respects:

the signal is sampled every 25 ns, providing in- formation on the pulse amplitude as a sequence of numbers, and the measurements are not linear due to the signal compression. In the present system, the trigger is not synchronized with the ADC clock, so that the time jitter is uniformly distributed in a clock period. In future applications at collider experiments, the clock will be phase-locked with the beam crossing time so that the jitter will be

much reduced. The analysis thus requires two steps. The first

step is to construct a lookup table for each channel to linearize the measurements. The construction of lookup tables requires in turn a detailed pulse shape reconstruction. This is described in the remainder of this section. The second step is to combine the samples of one channel to obtain an estimate of the energy released in each channel. This is discussed in the next section.

The calibration was performed using charge in- jection pulses. During the data taking period there was one dedicated run taken with PPG charge

104 2. Ajaltouni et al. JNud. Instr. and Meth. in Phw. Res. A 403 (1998) 9X-l 14

4-2 I I I

8

9 4

PPG trigger

c T -6- 1 2 I I I

8

?

PPG HV

ADC IYl I’)? 200

Fig. 6. Layout of the PPG system.

injection with 14 different pulse amplitudes. A few cuts were applied to the raw data to remove events with a pulse peak outside sample 17 through 24 and with amplitudes far from the mean or too small (< 5 ADC counts). Approximately, 600 events per PPG amplitude were recorded for channels 81 through 116, 500-550 of which survived the cuts

(see Fig. 7).

4.1. Pulse shape reconstruction

Provided that the shaper is sufficiently linear, and that neither the shaper nor the compressor exhibits time slewing effects, the shape of the pulse is independent of the amplitude.

By “shape” we denote the functional form of the pulse, modulo scaling in amplitude and translation in time. The scaling corresponds to different re- leased charge, and the translation to different time of flights (depending on different orientations of the calorimeter). These two quantities can be estimated for each event and in the following we concentrate

on the measurement of the scaling factor, that can be unambiguously converted to energy.

In this analysis the stored samples per event (time frames) are assembled to obtain the average pulse shape following an algorithm first used in Ref. [ 133. Fig. 8 shows the average time frames for each amplitude for a given channel, before and after decompression with a preliminary lookup table

Z. .4jaltouni et al.lNucl. Insrc trnd Meth. in Ph>g. Rvs. .A 403 (1998) 9X-I I4 105

L .

Fig. 7. Impact points and direction of the beam in the five rtms

consldered in this analysis.

600

measured in the laboratory. Pedestals are cal-

culated from a few (8-10) samples preceding the

pulse and subtracted from the compressed measurements. The sampling of the pulse shape in Fig. 8 is rather coarse compared to the width of the pulse and the distributions of the sample ampli- tudes are widened because of the random phase of the FERMI internal clock with respect to the trig- ger. A much finer sampling of the shape can be obtained using a phase estimator and rebinning the samples accordingly.

The phase estimator is constructed by comput-

ing the slope between two samples straddling the peak. We take our phase estimator as S = (s( 19) - s(23))/.~(21) where s(n) indicates the amplitude of the sample II. The choice of 21 as the peak sample is dictated by the delay fixed by the hardware. The resolution of this estimator of the phase is limited by the quantization of the ADC (times the derivative of the pulse at each point along the curve), statistics and noise. We have. somewhat arbitrarily, chosen to subdivide the bins into subbins of 1 ns.

Fig. 9 shows the amplitude--phase correlation in a 2511s interval around the peak for two PPG levels. for compressed and decompressed data. Such correlations are used to construct Fig. 10,

TILECAL PPG data - Ch. 115 Y 31. ‘: s- _ Charge ampl. 2-7 i

: 3oc +‘,

/Y 600

Charge wnpl. 8- 15

ThWYSlkS Compressed pulses Decompressed pu ses T

he/l5”S Decompressed pu T a!?“’

Fig. X. Average frames for compressed (left) and decompressed (middle and right) PPG pt~lses.

106 2. hjaltouni et a/. /Nucl. IPISW. und Metir. in Pigx Res. A 403 (IYYM Y&I I4

TILECAL PPG data - Ch. 115 3 ;

a 2 16 r

# 460 - f < PPG pulse 6 4 155 r

PPG pulse 6

440 - 15 7 . . . .

g;jap:?z%:;a:+..... . . L .:..~;;.i;.;o.;!:::b:.;;1..:::.: . ..m.. . . ..(10.0..

420 - . . . ..“..:.:p;:;,.. 14.5 7 ‘~~~~~.a~~~~~.~~~.~‘~ . . . . . . . . . ...&&... . . . ..a&’ . *...

. . . ..m.... . . ..-..Elm. .a..0 . 14

Amp1 vs Slope

PPG pulse 15

S d

lI

1000 ; 500 - . . . .

971 7 * . . .: :...:. ! -. :‘:. . . . . . . _ .i’::::.:“‘~O’“~.91~i~~~~~~~~~~~~~~~~

480 _ . . .:’ . . . . : . . . D . . . . h, . o . . . .m... ~._.~;o_o.~:D’ ::. *.amm em

. . ..o q . . D.nom.D.0.. D . . . . . . ..P..g.I.*B.:!: - . . . . ..D.D.O... ..a.... q

950 : . . m q * ...~s~ ., :a:..: ;.;......~:‘~.: q . ..D.. m :. . ;:

. . . . , 460 -..“;:3. ..*: . : .: . . . . ., : :.

. . . 921 :

440 - 900 :

Fig. 9. Peak amplitude versus slope (phase estimator) for compressed (left,

6 (top) and I5 (bottom).

in ADC counts)and decompressed (right. in PC’) PPG pulses

where we see the same data as in Fig. 8 reconstruc- ted with a binning of 1 ns for all amplitudes. We note that all curves cross the zero line at the same point. In the lower two plots the pulses have been normalized to the same peak value to illustrate the similaritites of the shapes after decompression. More information on this approach can be found in

Ref. [13].

4.2. Methods for deriving the lookup tables

The lookup table should provide an inverse of the compression function so as to restore linearity with quantization errors small compared to the resolution of the calorimeter.

The most straightforward approach is to per- form quasi-static measurements in the laboratory using a step function at the input and recording the step amplitude at the output. If the input can be controlled with sufficient precision, the full lookup table can be reconstructed.

An implicit assumption underlying this approach is that the value of the compressor output at a given time depends only on the value of the compressor input at the same time. That is in general not true because of the bandwidth limitation of the compressor and. more important, of its slew rate limitation. This implies that the compressor has a non-trivial and non-linear transfer function and that a quasi-static measurement may not be

107

Fg. 10. Reconstructed pulse shapes. Compressed (top left1 and decompressed ltop nght). The decompressed pulses art: notmnlized to

the11 peak valws (bottom). Due to noise. the peak value IS nnt sharply defined for IOU. amplitudes. thus the diweparw between the

comes m the lower left plot.

TILECAL PPG data - Ch. 115

300

200

100

0

600

500 1000 isnn

Decompressed Pulses Time/1 ”

PPG pulses 5- 15

400 600 x00 100

Normalized Time/I 11s

adequate, since the compression function could depend on the input pulse shape. Another ap- proach is therefore to pulse in situ the electronics chain with a charge injection system that closely mimics the pulses from actual data.

If we could choose the amplitudes of the charge injection system with adequate granularity and control the phase of the injected pulse with respect to the ADC clock with arbitrary precision. the amplitude and shape dependence of the com- pression function could be studied with great precision.

In the present set-up there were however only 14 different amplitude settings and the timing between

the pulse and the ADC clock could not be hxed or measured directly, but only estimated with help of the phase estimator defined in Section 4.1. We had

thus to use more advanced methods, using the entire pulse. to extract the required information from the calibration data.

The different gains of each individual compressor could vary slightly due to spread in component values, mostly in the supporting circuits. The values of the cutoff voltages could also vary. ‘To the first order these effects can be taken into account by taking a model lookup table Vmodel measured in

108 Z. Ajaltouni et al. JNucl. Instr. and Meth. in Phw Res. A 403 (IYYN) 9X-114

TILECAL PPG data - Ch. 115

I I I i I t I I i I I I I i t o II i I A I I i , 0 0.5 1 1.5 2 2.5 3

LUT table and PPG data (dots) PPG elxlrge

$ 1000 7

g 800 - 4

600 :

400 :

200 r

_~/:,.:/:-:;;:_-_.:~ ~*I-

0 i-- *-.- I I k 10 -3 lo3 10 -I

LUT table and PPG data (dots) PPG Ch&

Fig. 11, Model LUT (higher curve) compared to stretched LUT (lower curve) from three-parameter fit in linear (top) and logarithmic

scale (below). PPG pulses are shown as fat dots.

the laboratory quasi-statically as mentioned above and distorting it slightly, by stretching and translating.

In this method we use only the peak amplitude values and the nominal charge of the PPG pulses. A parabolic fit is made to the peak region of the pulse shape to find an estimate of the peak value at zero phase. The extrapolation of the PPG peak amplitudes towards zero intercepts the charge axis at a non-zero value, q,,, which is the first parameter. The model lookup table, converting ADC-values into charge, is then linearly stretched in the charge and ADC variables, defining two more parameters, z and 8, respectively. The distance between the stretched lookup table V(k) = uV,,,,,(@) + q,, and the PPG points is minimized with respect to these three parameters

min x2 = 1 (~~model(p&Xin) - (ClPPGn - %J))2.

a.8.q” n

The result is displayed in Fig. 11 where the un- stretched and stretched model lookup table are plotted together with the measured PPG mean pulse peaks. The PPG data do not span the dy-

namic range of the compressors as well as the test beam, thus the lookup table is linearly extrapolated up to the highest values. This introduces an addi- tional uncertainty for the channels measuring the highest energy in the test beam.

4.2.2. Pulse shape comparison A more sophisticated method uses the fact that in

a perfectly linear system the shapes of the pulses are identical, modulo a scaling factor. In case of the PPG data the scaling factor is known as the charge injected; it is labelled E,.

In the procedure outlined below we assume a knowledge a priori of the lookup table l’(k) for a limited range of ADC counts. For this we use laboratory measurements of a typical channel. This choice is not critical, since for low values of the ADC counts the lookup table is linear.

Denote the pulse shapes, reconstructed as de- scribed in Section 4.1, s,(i), where i indexes the time in bins of 1 ns, and n enumerates the different PPG amplitudes. We need to choose one such pulse as our reference, small enough to reside entirely within the first slope of the lookup table but large enough

to stand clear of noise; this pulse is referred to as s&i).

Divide the ADC-axis into intervals between successive peak values of s,,, k,,,,, = Lmaxi s,,(i), where Is,(i) represents the ADC quantized value corresponding to s,(i). For each such interval (1;,,,,,,, _ ,,l\,,,ar,n] we use s,, and s,,~ to determine the updated lookup table.

The reference pulse s,,&i) is scaled up to the scale of the pulse under consideration. Because of shape invariance, this should correspond to the compres- sor input when it produces the compressed pulse s,, on the output:

where V denotes the true (ideal) lookup table,

and &et- the (injected) charge of the reference pik.

To build the modified lookup table. V,,,,(k), we need to average over all time steps (i) such that Is,,(i) = k. w e re utre at least one value from the q

leading edge and one from the trailing edge to contribute to the determination of each ADC value. Since s,(i) is discrete in i, it might skip ADC-values on either edge of the pulse. Therefore, we define the extension of s,(i) into the continuous domain by interpolation. s,,(r). Finally. we get

P,,,,( Ii) = ’ E” F, ( V(Srrf(flrading)) + v(sref (f7railing))). rc,

Because of slew rate problems present in the compressor used in the 1995 test beam run. the invariance of the pulse shape for different amplitudes is only approximate. Parts of the pulse rising or falling at different rates are compressed slightly differently. The effect is to give separate compression functions for the rising and falling edges of the pulse and to add amplitude dependent distorsions.

The lookup table built above is the one minimiz- ing the pulse shape dependence on the amplitude. according to the least square minimization method.

The residual dependence of the pulse shape on the amplitude might give a non-linearity for any given amplitude estimator which may take different forms for different estimators. The approach taken

here is to compute the value of a given estimator fat

each PPG step using the V,,,, above. The values so calculated (F,,) are used to iteratively refine the correction factors for the lookup table (applicable for the given amplitude estimator):

Frrf 6, L, = E F.

ref ,I

As a result of this operation, discontinuities may appear in the lookup tables at the interface point between the ADC values linearized with two differ- ent pulse levels. as the factors L,, and L,,_ 1 are in general not equal. In order to correct for this effect, a factor X, is defined as

and ~,i” is recalculated iteratively as

V,i”(k) = L’,i”(l, - 1) + Y” ( byj,,,(k) - b’“,,v(/i - 1)).

When the full l’lin has been recomputed. new values for the F,, are obtained.

Using the new F,,, the above procedure is repeat- ed, always starting from the original t’,,,,V. After three iterations, the C’,,,, obtained is taken as tinal result.

5. Energy estimation

The energy content (or pulse amplitude) of each single cell is estimated from a subset of the 60 samples of a FERMI time frame; this procedure is called filtering. The optimum filtering algorithms both with linear and non-linear filters have been studied in detail in Refs. [14--191. Linear Finite Impulse Response (FIR) filters consist of a finite number of coefficients multiplying the samples. Here we consider only adders, filters with unit coefficients.

From a general point of view. there are foul dominant sources of degradations in the energy measurements of a sampled system: the electronic

110 Z. Ajaltouni et al. /Nucl. Irish. and Meth. in Phvs. Res. A 403 (1998) 98-I 14

noise, the quantization error, the time jitter of the event and the pile-up coming from other events. In the condition of a test beam, the last term can be made negligible, controlling the beam intensity and removing overlapped events. For pulser events, this source does not exist at all.

The measurement of energy in presence of differ-

ent sources of noise may lead to conflicting require- ments on the filters. Generally speaking, long filters are required to suppress the contribution from jit- ter, while shorter filters may be more appropriate to suppress the electronic noise. The quantization error in presence of a non-linear quantization func-

tion follows a complex pattern strongly dependent on the details of the pulse and of the filter.

A simple, but quite effective, approach is the use of adders, varying the filter length. An adder sup- presses the time jitter influence if it is long enough to include both the leading and the trailing edge of

the pulse. Therefore, for each event, the samples are decom-

pressed using the lookup table. Then the pedestal is

calculated from the average of the first few (S-10) samples. After pedestal subtraction, the adder is slid along the decompressed pulse until it reaches the maximum. Adders of lengths 1-25 have been

considered.

6. Measurement of resolution

6. I. Single-channel resolution

The intrinsic resolution of the two calibration methods is measured through the resolution of the charge injection data, using the energy estimates described above. We also look at the deviations from linearity of charge injection data, defined as the residuals of a fit of the averages of the energy estimates versus the charge injection amplitude.

In Fig. 12 the resolution is plotted versus adder length for three different amplitudes, using pulse shape comparison lookup tables. The dependence of the resolution on the adder length is different for different amplitudes, due to different combination of the above-mentioned error sources. For low am- plitudes, the dominant source of uncertainty is noise, that grows with the adder length. For larger pulses noise is less significant, hence time jitter and

quantization errors are predominant. In Fig. 13 the resolution is plotted versus ampli-

tude for adder lengths of 5 and 11. Except for the smallest amplitudes, the intrinsic resolution is al- ways below 0.44%. It is difficult to discern any difference between the three-parameter fit method (J) and the pulse shape comparison method (*).

10

i3L-J--+ 0 10

adder len@h

Channel 85

nchler length adder length

Fig. 12. Resolution vs. adder length for three different PPG amplitudes. using pulse shape comparison lookup tables.

III

0 3PF ? y PSC

Y

a

0 3PF

y PSC

J ” 1 ’ 1 ’ “1 1 ’ “1 I”“1 I) 0.25 0.5 0.75 1

Fig. 13. Resolution vs. PPG amplitude for adders of lengths 5 and 1 1

30

20

in i ?

Entries 243

Mean 0.3724E-02

RMS O.l023E-02

Fig. 14. Resolution for all channels with adders of length I I using three parameter fit (left) or pulse shape c~mp;lr,son (ryht). PPC;

pulsch helow an amplitude of (1.07 pC have been cut.

In Fig. 14 the resolution of all channels is histog-

rammed, for the case of an adder of length 11, using the two different lookup tables. The distributions are not significantly different.

In Fig. 15 the deviation from linearity vs. ampli- tude for a few channels is plotted for the two methods. In Fig. 16 the deviations from linearity for all channels are histogrammed for both

methods. The pulse shape comparison clearly gives a better linearization than the three-parameter fit.

fi.2. Event sample selection

For the analysis those C runs at 300 GeV that were contained within the FERMI-equipped channels were chosen. These gave the smallest

112 2. &dtouni et al.~Nucl. Instr. and Meth. in Phts. Res. A 403 (1998) 9Sll4

5 0.02 .c 3 5 0 0.01

d

0

-0.01 0 0

* PM

-0.05 L 0 0.5

charge (p

Channel 85

g 0.02

:!ool e .

0

-0.01

-0.02

-0.03

-0.04

-0.05

0

0 3PF * PS(

c 0.02 0

z ‘5 0 . 01 w

0

-0.01

-0.02

-0.03

mm rn@ 0

0 3PI

0 0.5 0 0.5 charge

@C: charge (p’

Channel 89 Channel 114

Fig. 15. Deviation from linearity vs. amplitude for three different channels.

3PF clenatwn

80

70

60

50

40

30

Eotries 324

Meun 0.4037E.03

UMS 0.4587E.02

-0.04 -0.02 0 0.02 0.04 deviation

PSC

Fig. 16. Deviations from linearity for all channels. PPG pulses with an amplitude below 0.0’5 pC are removed.

intrinsic fluctuations and made the most sensitive comparison of the two read-out systems.

In order to remove the electron and muon con-

6.3. Resolution with Fermi and the standard electronics

taminations from the beam we demand that be- tween 60% and 95% of the energy be deposited in the first two sampling depths of the calorimeter and that the total energy be above a threshold.

The most straightforward method of comparing the two read-out systems would use the energy resolutions obtained using the channels that were equipped with both types of electronics. Due to the

large leakage into channels without FERMI (most- the Cs,,J term gives a sizeable contribution while

ly into the neighbouring modules) the fluctuations C ,eakage is comparably smaller.

of the deposited energy is quite large. The quality of the electronics and our calibration

methods is measured with the signed quadratic difference.

To account for the leakage we reconstruct the energy released in the 173 channels with standard read-out electronics only, in addition to the 27 equipped with FERMI. In all runs the fraction of the total energy deposited in the FERMI equipped channels varies between 75% and 90%.

The resolution in both cases can be written as a quadratic sum of one energy dependent term and three or four constant terms. The energy-dependent term is the intrinsic spread in the measurements, depending mainly on the calorimeter, and the con- stant terms are contributions from leakage. from the electronics calibration errors, and, when con- sidering the sum of standard and FERMI channels. from interchannel calibration errors. Noise contri- bution is small at the energies considered and there- fore is not included:

between the resolutions. where negative sign of 6 indi- cates that the standard term under the square root is larger than the FERMI term. This gives an estimate of the FERMI electronics contribution to the resolu- tion. In order to assign an error to 3. the high correla- tion between the measurements with FERMI and the standard electronics has to be taken into account.

6.4. ,Measutvd resolutiorls

In Table 2 and Table 3 we see that the three- parameter fit method (“stretching”) is slightly worse compared with the standard read-out electronics. Most likely that is due to the limitation of linearity in the lookup table shown in Fig. 16. On the other hand, the method based on linearized pulse shape comparison performs significantly better than the standard electronics. at least for an adequate filter length. This is demonstrated in Table 3. The main reason is likely to be the higher control on linearity guaranteed by this method.

where the subscript S denotes standard read-out electronics and F denotes FERMI.

When comparing only 27 channels, the

Cs173 term does not contribute while lateral leak-

age in the q5 direction makes Cleakagc large; this term is however in common between the two different read-out electronics. When summing 200 channels

The performance of FERMI can be summarized in a quadratic reduction of 1 ‘>o of the constant term in the resolution.

Similar analyses at lower energies confirm this result.

Table 2

Resolutions tin ‘~1 for standard electronics (stand.). and FERMI with the look-up tables reconstructed with the three-parameter tit

(PF) and the pulse shape comparison (PSC) methods for 5-adder and I I-adder for five runs (cf. Fig. 7). usmg 200 ch;lnnel\

Run

Stand.

33484 33485 33486 33487 33489

5.16 i 0.06 5.73 + 0.08 4.36 * 0.05 4.36 i 0.05 4.67 ?_ 0.06

?PF 5 5.55 + 0.07 6. I3 * 0.09 4.x4 _t 0.06 4.75 & 0.06 1.7: * 0.06

‘PF 11 5.39 f 0.07 5.96 + 0.09 4.61 i 0.05 4.5x * 0.0’ A.69 If- 0.05

PSC 5 5.14 + 0.06 5.81 + 0.08 4.4 I f 0.05 4.42 + O.I)Z 171 * 0.05

PSC II 5.04 * 0.06 5.59 * 0.07 4.3 1 & 0.05 4.?? + (1.05 4.6 I * 0.05

114 2. Ajaltouni et al. /Nucl. Instr. and Meth. in Ph_vs. Res. A 403 (19YFi) 9X-114

Table 3

Quality measure of the read-out, 6, expressed as the signed quadratic difference with the standard resolution. for the look-up tables

reconstructed with the three parameter fit (3PF) and the pulse shape comparison (PSC) methods for 5-adder and I l-adder for five runs

(cf. Fig. 7). using 200 channels

Run 33484 33485 33486 33487 33489

3PF 5 2.03 i 0.06 7.19 * 0.07 2.10 * 0.05 I.89 ) 0.06 0.77 * 0.07

3PF 11 I .56 k 0.05 I .67 f 0.07 1.48 + 0.05 I .42 * 0.07 0.48 & 0.10

PSC 5 - 0.44 * 0.15 0.98 * 0.10 0.63 + 0.10 0.71 kO.14 0.65 k 0.07

PSC 11 - 1.10 * 0.05 - 1.21 + 0.07 - 0.68 & 0.08 - 0.56 _ i 0.17 ~ 0.73 + 0.06

7. Summary

A module of the prototype of the ATLAS hadronic calorimeter has been successfully tested with a prototype version of the FERMI read-out system including a compressor and a sampling ADC.

The charge injection system has been used to calculate separately for each channel lookup tables that minimize amplitude-dependent distortions and non-linearity. These techniques in conjunction with the use of linear adders to process the sampled data, reduce the constant term in the energy resolu- tion as compared to the one obtained with stan- dard integrating ADCs.

The FERMI read-out system performs well and is a good candidate for a calorimeter read-out sys- tem at LHC. For an optimal energy determination the system requires a detailed pulse shape calib- ration.

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